Perturbation theory for multiphoton ionization without knowledge of the final-state wave function

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 60, Issue 2, 1999, Pages 1280-1286

  Shakeshaft, Robin ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038248623     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.60.1280     Document Type: Article

References (27)

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21. To see that Eq. (12) is correct in the limit (Formula presented), we first calculate the rate (Formula presented) in terms of the amplitudes (Formula presented) for the atomic system to absorb one photon and lose one electron, with the residual ion left in the state (Formula presented). In position space the function representing (Formula presented) behaves for large values of the photoelectron coordinate r as (Formula presented); see Eq. (16). Hence, setting (Formula presented), the photoelectron probability current density at large r is (Formula presented), where we have dropped oscillating terms arising from interference since they vanish upon integration over a sphere of large radius. Integrating over a sphere of surface area (Formula presented), the net current is (Formula presented)Now consider the right-hand side of Eq. (12). Writing (Formula presented) as a volume integral, we need only be concerned with the divergent part of the integral since the finite part vanishes after multiplication by (Formula presented). The divergent part comes from the nonoscillating part of the integrand in the region of large r, and noting that (Formula presented) we have (Formula presented)The integration over solid angle gives (Formula presented) and performing the integration over r yields (Formula presented), thereby confirming Eq. (12).
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